Apart from saying that her name may or may not have been Elizabeth, I get to a dead end. One assumes that she was born around Portarlington about 1790 to 1800, probably at Clonsast, as that was where her husband came from.
There are still available parish registers for the Portarlington area, and something may still be found. The only course open is to try to get her maiden name from a marriage to George Watson, then work back to birth.